Explain how 7/10 and 70/100 are equivalent decimals

Answers

Answer 1
Answer:

It is proved that the given decimals are equivalent decimals.

What are equivalent fractions? What is a mathematical function, equation and expression?

  • equivalent fractions : Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value.
  • function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
  • expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.
  • equation : A mathematical equation is used to equate two expressions.

Given are the fractions -

7/10 and 70/100

We have the following fractions -

A = (7/10) = 0.7

B = 70/100 = (7 x 10)/(10 x 10) = (7/10)

B = (7/10) = 0.7

It can be seen that fraction A equals to B.

Therefore, it is proved that the given decimals are equivalent decimals.

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Answer 2
Answer:

Step-by-step explanation:

7/10 in percentage form is 70%

70/100 in percentage form is 70%

Simple as that


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The question is: 5 < b - 3

Answers

Answer:

8 <b

Step-by-step explanation:

5 < b - 3

Add 3 to each side

5+3< b-3+3

8 <b

Answer:

8 < b

Step-by-step explanation:

1. Add 3 by both sides to eliminate the -3 on b - 3.

2. You get 8 < b.

Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg). Heavier cars tend to have lower fuel efficiencies (lower mpg ratings). Which variable (weight or fuel efficiency) is most naturally considered the explanatory (predictor) variable in this context? A. Weight B. Fuel efficiency

Answers

Answer:

Correct option: A. Weight.

Step-by-step explanation:

In regression analysis there are two kinds of variables: Explanatory and Response variable.

The explanatory variable are used to predict the changes in the response variable. They are also known as independent or predictor variable.

The response variable are observed for any changes caused by the explanatory variable. They are also known as the dependent or experimental variable.

In this case it is provided that heavier cars have lower fuel efficiencies.

It implies that there is linear inverse relationship between the variables weight of the car and fuel efficiency.

The response variable is the fuel efficiency and the explanatory variable is the weight of the car. Since the weight of the car is used to determine the fuel efficiency.

Thus, the explanatory variable is the weight of the car.

Final answer:

The explanatory variable in this context is the weight of the car, as it is used to predict or explain the car's fuel efficiency.

Explanation:

In this context, the most naturally considered explanatory or predictor variable would be the weight of the car. This term is used to denote the variable that is used to predict or explain changes or variations in another variable. In this case, the weight of the car is used to predict or explain the fuel efficiency (measured in miles per gallon). For instance, if the weight of a car increases, we would expect the fuel efficiency to decrease (lower mpg) because heavier cars often require more energy to move, which in turn results in higher fuel consumption.

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During migration a butterfly can travel 30 miles in 1 hour. Which graph best represents y the number of miles a butterfly can travel in x hours

Answers

The linear equation that models this situation is y = 30x

What is an equation?

An equation is an expression showing the relationship between numbers and variables.

The slope intercept form of a straight line is:

y = mx + b

Where m is the slope and b is the y intercept.

The standard form of a straight line is:

Ax + By = C

Where A, B and C are constants

Let y represent the number of miles a butterfly can travel in x hours. The butterfly can travel 30 miles in 1 hour, hence:

y = 30x

The graph is attached

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An attacker at the base of a castle wall 4 m high throws a rock straight up with speed 7.5 m/s from a height of 1.5 mabove the ground.
(a) Will the rock exceed the top of the wall?
(b) If so, what is its speed when it reaches the top of the wall?
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(c) If we don’t want the stone to exceed the top of the wall (we want the top of the wall to be the maximum height)
what the initial speed that the stone must have?

Answers

Answer:

a) Yes, b)v\approx 2.686\,(m)/(s), c)v_(o) \approx 7.002\,(m)/(s)

Step-by-step explanation:

a) The maximum height reached by the rock is:

\Delta y = (\left(0\,(m)/(s) \right)^(2)-\left(7.5\,(m)/(s) \right)^(2))/(2\cdot \left(-9.807\,(m)/(s^(2)) \right))

\Delta y = 2.868\,m

y = 1.5\,m + 2.868\,m

y = 4.368\,m

Yes, the rock will exceed the top of the wall.

b) The speed when the rock reaches the top of the wall:

v = \sqrt{\left(7.5\,(m)/(s) \right)^(2)+2\cdot \left(-9.807\,(m)/(s^(2)) \right)\cdot (4\,m-1.5\,m)}

v\approx 2.686\,(m)/(s)

c) The initial speed required so that stone does not exceed the top of the wall is:

v_(o) = \sqrt{\left(0\,(m)/(s) \right)^(2)-2\cdot \left(-9.807\,(m)/(s^(2)) \right)\cdot (4\,m-1.5\,m) }

v_(o) \approx 7.002\,(m)/(s)

Create and solve
an equation with
2 variables(x).

Answers

Answer:

5x-2=3x+4

x=3

Step-by-step explanation:

Hope I helped!

HELP MEE ILL MARK BRAINLEIST

Answers

Answer:

3x-3 I think that's it.

Step-by-step explanation:

Answer:

The vertex is (1, -4)

Step-by-step explanation: